# How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc

I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy.

Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do this is by taking the standard deviation on the daily returns.

However, I want to use an alternative estimator (see Yang Zhang) which requires as input the Open High and Low prices. How can this estimator be applied to estimate the volatiliy of my portfolio?

• do you have the intra-day opens, highs, and lows? – David Addison May 11 '17 at 17:54
• Of the original Time series yes but not of my portfolio.. solely daily returns – JohnAndrews May 11 '17 at 18:50
• Why not implement a rolling 4-period window in which there will always be a open, high, low, and close? Of course, this would need to recognize the possibility that the open and close can be the high and/or low. You could then average the errors to get an estimate of variance. There are more ways to skin this cat... this is just one idea. – David Addison May 11 '17 at 19:34
• Not getting what you mean. How do you for instance link exactly the Open with the return of my portfolio which is realized at the end of the day? – JohnAndrews May 12 '17 at 11:19
• I was wondering if you had a chance to review the model I attached and, if so, whether you have any questions. – David Addison May 16 '17 at 7:03

• The Yang-Zhang volatility estimator requires the intraday high and low.

The logical conclusion would be that you cannot use the Yang-Zhang estimator to estimate your portfolio's volatility.

### Discussion

The idea behind Yang-Zhang and other advanced volatility estimators is that intraday movements provide additional information. By utilizing this information, they generate more precise volatility estimates from the same number of days of data.

• But you do know the High, Low and Close – JohnAndrews May 16 '17 at 7:42
• @JohnAndrews Of the stocks, but not the portfolio, right? If your portfolio is 1 share of Google, 1 share of Apple. How can you figure out what the intraday high of your portfolio is? It's not the high of Google plus the high of Apple because the highs may not have occurred at the same time. You need the full intraday path of Google and Apple to get the intraday high of your portfolio. – Matthew Gunn May 16 '17 at 7:51
• So the only volatiliy that you can estimate of your portfolio is using the Historical Std Dev. That cant be right no? – JohnAndrews May 16 '17 at 7:55

There are a few different ways to approach this problem.

One possibility is to transform your daily price/return data into weekly open, high, low, close data. You may then calculate the Yhang-Zhang or other suitable OHLC variance estimator (e.g., Garman-Klass, etc) as per the canonical approaches.

This approach is enumerated in this the attached spreadsheet. In the spreadsheet, given only daily close data and dates, a weekly OHLC series was constructed. The YZ estimator was then taken over the entire data range.

Another possibility is to perform a moving time-series analysis, which may be more appropriate if one believes that the variance is non-stationary. I've had success incorporating YZ into autoregressive moving average (ARMA) models, such as generalized auto-regressive conditional heteroskedasticity (GARCH) models. In order to do so, one starts by calculating the YZ error over each interval.

Note: The weekly YZ estimator is not likely to result in a more efficient estimate than the daily close-to-close estimator. It will, however, provide an alternate measure of dispersion.

• Why transform to weekly open? I still dont see the link with my portfolio returns. – JohnAndrews May 16 '17 at 7:41
• Transforming the time-series is the only way with which I am familiar to tease out OHLC data points. The link provided simply refer to a sample price data -- I don't have your portfolio returns. – David Addison May 16 '17 at 15:33